Text-to-Image (T2I) diffusion models have shown impressive results in generating visually compelling images following user prompts. Building on this, various methods further fine-tune the pre-trained T2I model for specific tasks. However, this requires separate model architectures, training designs, and multiple parameter sets to handle different tasks. In this paper, we introduce UniVG, a generalist diffusion model capable of supporting a diverse range of image generation tasks with a single set of weights. UniVG treats multi-modal inputs as unified conditions to enable various downstream applications, ranging from T2I generation, inpainting, instruction-based editing, identity-preserving generation, and layout-guided generation, to depth estimation and referring segmentation. Through comprehensive empirical studies on data mixing and multi-task training, we provide detailed insights into the training processes and decisions that inform our final designs. For example, we show that T2I generation and other tasks, such as instruction-based editing, can coexist without performance trade-offs, while auxiliary tasks like depth estimation and referring segmentation enhance image editing. Notably, our model can even outperform some task-specific models on their respective benchmarks, marking a significant step towards a unified image generation model.